Mathcast #3: Quick multiplication of two 3-digit numbers
Here's the You Tube Video that follows up Mathcast #2: Quick multiplication of two 2-digit numbers. The algebra of cross-multiplication explains how this method is derived.
If you enjoy this video check out all of the Wild About Math! mathcasts.
Mental Math and slowing down aging
I can't prove this but I bet that doing lots of mental Math can help slow down aging. In studying a number of techniques for doing fast arithmetic I notice a number of mental skills at play:
- Pattern recognition. Many tricks involve recognizing and exploiting a pattern.
- Visualization of processes. Multiplying large numbers together requires you to hold a mental image of multiple steps.
- Alertness. Falling asleep will cut way down on your efficiency in every technique!
- Mental speed. Impressing your friends will require you to develop speed in your technique.
- Memory. Efficient arithmeticians memorize more Math facts than others. Some people, for example, find memorizing the squares of all numbers up to 25 to be helpful in certain techniques. Also, you often need to maintain a running total in your head and keep track of carries..
- Concentration. When multiple steps need to happen in a sequence your powers of concentration will improve.
A friend and I were discussing how mental Math could help maintain the plasticity of the brain, its ability to reorganize itself in response to new information. She thinks that doing a number of cross-multiplications every day can keep the brain active as we age. I agree.
Diabolical geometry problem
While surfing the web I discovered this: World's Hardest Easy Geometry Problem. There's actually two geometry problems on the page. Apparently these are classic problems that have tortured students for a long time. I spent a little bit of time working on the first, and even looking at the two hints, and didn't solve it.
Give it a try.
The algebra of cross-multiplication
A few people were underwhelmed with my video on how to multiply together a pair of 2-digit numbers without writing down partial results. They didn't see a time savings. Fair enough, although not needing to write anything but the three (or four) digits of the answer can be a nice time savings and a source of smugness for many.
Next week I'm going to produce some more mathcasts. The first one will show how to multiply together a pair of 3-digit numbers using the cross multiplication approach. I think that will impress more people.
There's a general approach to these multiplications I want to teach you. If you understand the algebra behind this approach you can derive the steps for multiplying together numbers containing any number of digits. However, I'll warn you that beyond 5 digits this approach, and any other approach that works for any numbers and not just special cases, will really work your mental muscles.
Carnival of Homeschooling features four Math articles
Carnival of Homeschooling #101 is out at Dewey's Treehouse. This is one of my very favorite carnivals as it's always really well done.
Four Math articles were featured and these descriptions were copied from the Carnival page:
1. Let's play math presents Fraction models, and a card game
2. Mandy presents Teaching Math Using Exercise posted at Building Blocks Blog.3. The Homeschool Math Blog presents Pan Balance Problems to Teach Algebraic Reasoning. "This post includes a FREE gift: download a whole lesson from my upcoming book of some pan balance (or scales) problems where children solve for the unknown."
4. Wild About Math! presents Mathcast #2: Quick multiplication of two 2-digit numbers.
Numerical memory in young chimps vs. adult humans – guess who wins?
It's reminiscent of those Planet of the Apes movies. Apes are smart. Humans are stupid.
ScienceDaily just ran this article: Young Chimps Top Adult Humans in Numerical
Memory. Young chimps and adult humans played this game where some numbers were displayed on a screen in some, I'm-sure, hard to remember order for, I'm-sure, not very long. Then the player had to identify which numbers were where, and in what order. Gulp! I'm glad I wasn't recruited for this game. I'd have put the whole human race to shame. I wonder what consolation prizes the humans got.
State of the blog address and goals for 2008
Just two months after starting this blog, and a little over a month after quitting my job to do "something different" I'm finding this creative expression to take on a life of its own in some very exciting ways that I'd like to share.
- Impress your friends with mental math tricks has become a "runaway bestseller" in a way I never would have imagined and has put Wild About Math! on the map. The Stumbleupon and Digg communities have really taken to this article that I thought was nice but never ever imagined would go viral. In the last 22 hours that article got viewed nearly 46,000 times and I believe it made the front page of Digg. Stumbleupon traffic has resulted in over 75,000 views of this article in the last couple of weeks. Del.icio.us, Mental Floss, and Shoutwire have also brought a significant number of readers to the article.
- I like to respond to as many comments as possible. I've fallen behind. I intend to catch up as there's some very valuable content in many of the comments.
- Overall, activity in the blog is buzzing. RSS readers are up. Technorati authority is creeping upward and Technorati blog reactions are increasing, as are the number of comments and email subscribers. I have to admit that while my ego is enjoying the boost, part of me is just a bit overwhelmed. If a small fraction of the visitors from the social networking sites stay I'll be quite happy.
- I'm enjoying the contact I've made with Tim Fahlberg regarding mathcasts. Tim has introduced me to a couple of people and others have contacted me as well in this regard. I promise I will get back to you once my level of overwhelm drops a bit. I see 2008 as a big year for making Math movies as I believe them to be much more effective at conveying fun and accessiblity than mere text and images and I'd love to help build community among all of us who make mathcasts.
- I'll continue the focus on simple activities that inspire curiosity about Math in 2008. I'll make more movies about arithmetic tricks, and about innovative ways to enjoy Math.
- Time permitting, I'll be writing articles about some Math explorations I've personally undertaken and results I've found.
- I'd like to develop closer relationships with the Math bloggers as there are some outstanding people and great content out there and I've not made the time to connect. So, I'll be making contact in the coming year.
- I'll be exploring ways to derive some income from the blog. When I quit my job last month I decided I would make a living on the Internet. I just launched a second blog, FederatedSearchBlog.com, for my brother and former employer. I am being paid to write and maintain that blog. For Wild About Math! I will look for corporate sponsors, sell Math-related products that I strongly believe in and explore other sources of producing revenue. I may start a third blog and may build a new web-site specifically designed to produce revenue.
- On the topic of Internet income, I'm a member of the Blog Mastermind Community founded by an Internet entrepreneur, Yaro Starak. Yaro has an outstanding and highly ethical approach to making money blogging. Studying his free material and then becoming a paying subscriber of his online course and community has really opened my eyes to what it takes to make a living on the Internet. I have to say that it takes quite a bit of work to make money ethically online which is why I focus on ventures I'm passionate about. Yaro is closing the doors to new members of Blog Mastermind on December 10th (my birthday). If you're seriously interested in earning significant income online, contact me, read this letter or check out a sample lesson from the course. Yaro is quite thorough in his education. And, if you are wondering, yes, I earn a commission from Blog Mastermind memberships but I wouldn't advertise a program that hasn't personally benefited me.
I look forward to connecting more with more of you and to sharing the joy of Math!
What kind of Math can you do with gum drops and tooth picks?
I'm enjoying the process of discovering how a little Math can go a long way. Readers are enjoying mental Math tricks, Math magic, and other simple things that engage children of all ages to see Math with a sense of awe.
One of my very favorite Math web-sites is Antonio Gutierrez' Go Geometry, subtitled "From the Land of the Incas". I can't even begin to describe this site. It has the most beautiful illustrations of geomtric constructions I've ever seen plus a number of challenging geometry problems. One could easily get lost in this site, and spend many enjoyable hours exploring its many sections.
Absolutely hilarious way to calculate pi
While perusing Ben Webster's blog (which is a joint venture according to the blog's about page) for the current Carnival of Mathematics articles I noticed a link to this absolutely hilarious article titled How to Calculate Pi by throwing Frozen Hot Dogs. I immediately got the joke as there's a fascinating way to calculate pi by dropping needles randomly on lined paper so I laughed really hard. There's actually some real Math here once you get over how funny the article is. And this article got published in WikiHow. Very cool!
I'm always impressed by the great sense of humor of many Math geeks. Some of these Math blogs are quite entertaining, even if I can't follow half of the Math some of these folks write about.
I slept through the Carnival of Mathematics
A link came my way from the 21st edition of the Carnival of Mathematics. That's when I realized I had forgotten to submit a piece. Well, I'm hosting the next Carnival on December 14, so when I get a whole bunch of submissions (hint, hint) I'll surely remember to produce the next edition.
Check out the current Carnival. Ben Webster has a nice theme regarding the Carnival having turned 21 and there are 21 blogs participating. Coincidence or conspiracy theory?!? Plus, it looks like Ben actually read all of the submissions he published and wrote eloquently about each one. So, he's set the bar high for me as my whole carnival was going to be to just copy and paste the URLs of the submissions I received
Oh, the next Carnival is going to be #22. I'm open to suggestions for a theme around 22. 22 factors into 2 and 11. That's all I can think of at the moment. Help!
Please send your submissions to this email: ![]()
[ Update on 12/3: Please submit using the Carnival submission form. ]